scholarly journals Numerical Solutions of Neutral Stochastic Functional Differential Equations

2008 ◽  
Vol 46 (4) ◽  
pp. 1821-1841 ◽  
Author(s):  
Fuke Wu ◽  
Xuerong Mao
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Functional Differential ◽  
Stochastic Functional

scholarly journals Numerical Solutions of Stochastic Functional Differential Equations

2003 ◽  
Vol 6 ◽  
pp. 141-161 ◽  
Author(s):  
Xuerong Mao
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Functional Differential Equations ◽  
Convergence Theory ◽  
Stochastic Functional Differential Equations ◽  
True Solution ◽  
Linear Growth Condition ◽  
Mean Square Convergence ◽  
Functional Differential ◽  
Stochastic Functional

AbstractIn this paper, the strong mean square convergence theory is established for the numerical solutions of stochastic functional differential equations (SFDEs) under the local Lipschitz condition and the linear growth condition. These two conditions are generally imposed to guarantee the existence and uniqueness of the true solution, so the numerical results given here were obtained under quite general conditions.

scholarly journals Approximations of Numerical Method for Neutral Stochastic Functional Differential Equations with Markovian Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-32
Author(s):  
Hua Yang ◽  
Feng Jiang
Keyword(s):  
Differential Equations ◽  
Stochastic Systems ◽  
Numerical Solutions ◽  
Functional Differential Equations ◽  
Approximate Solutions ◽  
Markovian Switching ◽  
Stochastic Functional Differential Equations ◽  
Em Method ◽  
Functional Differential ◽  
Stochastic Functional

Stochastic systems with Markovian switching have been used in a variety of application areas, including biology, epidemiology, mechanics, economics, and finance. In this paper, we study the Euler-Maruyama (EM) method for neutral stochastic functional differential equations with Markovian switching. The main aim is to show that the numerical solutions will converge to the true solutions. Moreover, we obtain the convergence order of the approximate solutions.

Numerical Method of Hybrid Stochastic Functional Differential Equations with the Local Lipschitz Coefficients

2011 ◽  
Vol 267 ◽  
pp. 422-426
Author(s):  
Hua Yang ◽  
Feng Jiang ◽  
Jun Hao Hu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Lipschitz Condition ◽  
Numerical Solutions ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Local Lipschitz Condition ◽  
Functional Differential ◽  
Stochastic Functional

Recently, hybrid stochastic differential equations have received a great deal of attention. It is surprising that there are not any numerical schemes established for the hybrid stochastic functional differential equations. In this paper, the Euler—Maruyama method is developed, and the main aim is to show that the numerical solutions will converge to the true solutions under the local Lipschitz condition. The result obtained generalizes the earlier results.

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